Rivera recalled facing dominant Cleveland teams of the 1990s, when the Indians had one of baseball's most feared lineups with Jim Thome, Manny Ramirez, Kenny Lofton, Omar Vizquel and Albert Belle.
Ahead of McIlroy and four shots back on the leaders in a tie for third are Jeev Milkha Singh of India and Colombia's Camilo Villegas, with Denmark's Soren Kjeldsen and Spain's Alvaro Quiros joining Americans Jim Furyk, Charley Hoffman and Kenny Perry on 11 under.
Canadian Mike Weir and South Africa Ernie Els were on top for the international side as they beat Jim Furyk and Anthony Kim while Asian pair Yang Yong-Eun and Ryo Ishikawa recorded an emphatic victory, downing Kenny Perry and Sean O'Hair 4 and 3.